Improved results of nontrivial solutions for a nonlinear nonhomogeneous Klein-Gordon-Maxwell system involving sign-changing potential

This paper is concerned with the following system: {-Delta u+lambda A(x)u-K(x)(2 omega+phi)phi u=f(x,u)+h(x),x is an element of R3,Delta phi=K(x)(omega+phi)u2,x is an element of R3, where lambda >= 1 is a parameter, omega>0 is a constant and the potential A is sign-changing. Under the classic Ambrosetti-Rabinowitz condition and other suitable conditions, nontrivial solutions are obtained via the linking theorem and Ekeland's variational principle. Especially speaking, we use a super-quadratic condition to replace the 4-superlinear condition which is usually used to show the existence of nontrivial solutions in many references. Our results improve the previous results in the literature.